Why when solving equations and other things in math do you no consider the negative square root?

Well, the answer is that you are quite correct to say that you should consider both the negative and the positive square roots when you are solving algebraic problems. But that does not mean that both are necessarily valid solutions. They may be, but often one is superfluous, having been generated by the algebraic process involved in the calculation or by the limitations imposed by physical reality. You can't move backwards in time, for example, so negative values of time or time interval are not acceptable.

So the crucial word is 'consider'. Look at both values and judge whether in the context of the problem set, they both make physical sense. I answered a question here a day or so ago which gave two answers (from the quadratic formula) for the depth of a well down which a stone had been dropped. One was 70 m, the other around 100 km - don't get many wells that deep!

If you have obtained answers from algebraic equations, the other check is to substitute the options back into the starting equation. You should do that, in any case, to ensure that you haven't blundered somewhere, but where you have two options from a square root it quickly shows whether they are both valid (it is possible that neither is, but that is unusual).

You cannot have a negative square root. For example, there is no square root of -9. The reason is because there is no number multiplied by itself that equals -9. You can have cube roots, but not square roots. If you took Algebra 2 then you should have discussed imaginary numbers, which does give a way to solve problems such as the square root of -9.

Hope this helps.